“Exotic” hadron-hadron S-wave Interaction

Bing-song Zou

IHEP, Beijing

Outline

1. “Exotic” S-wave Interaction

Why interested ? How “exotic” ? Similarity between and N s-wave scattering

What’s the nature of the broad ? Why it appears narrower in production processes ? Why f0(980)’s peak width is so narrow ?

2.S0pp & I=1 S0pp near threshold enhancement

3. KS-wave near threshold enhancement in J/p K-vs p p p

1. “Exotic” S-wave Interaction Why interested ?

1) a fundamental strong interaction process and a necessary input for many reactions involving multi-pions

2) I=0 S-wave has the same quantum number of f0 resonances which include : /f0(600) (-model, exchange for NN interaction)

and the lightest glueball candidate f0(1500)/f0(1710)

f0

How “Exotic”

p p

CERN-Munich data: B.Hyams et al., Nucl. Phys. B64 (1973) 134.

Exotic I=0 S-wave

I=0 D-wave

I=1 P-wave

I=1 F-wave

(770)

(1690)f2(1270)

D.V.Bugg, A.Sarantsev,B.S.Zou, Nucl. Phys. B471 (1996) 59

phase shifts

inelasticity

“Exotic” S-wave interaction : broad background with narrow resonances as dips instead of peaks

p

I=0) (I=1/2)N(I=1/2)

Similarity for and N s-wave scattering

What’s the nature of the broad ?

Important role by t-channel exchange for all these processes

=0 = - 2 K

I=2 =1/2 = - 2 K

I=3/2

D. Lohse, J.W. Durso, K. Holinde, J. Speth, Nucl.Phys.A516, 513 (1990) B.S.Zou, D.V.Bugg, Phys. Rev. D50, 591 (1994)

Basic features of I=2 Interaction F.Q.Wu, B.S.Zou et al., Nucl. Phys.A735 (2004) 111

repulsive force by t-channel

attractive force by t-channel f2

Inelasticity by

S-wave

An important cause for hadron-hadron S-wave interactions appearing “exotic” is

t-channel meson-exchange amplitude has a comparable strength as s-channel resonance contribution for S-waves.

For higher partial waves, s-channel resonance contributiondominates.

Why broad appears narrower in production processes than in elastic scattering?

Tel= K / ( 1 - i K ) = K + K i K + K i K i K + …

Tprod= P / ( 1 - i K ) = P + P i K + P i K i K + …

el

prod

Tel from Bugg,Sarantsev,Zou Nucl. Phys. B471 (1996) 59

with pole at ( 0.571 – i 0.420 ) GeV

Tprod = Tel * P / K , K = tan

assuming P=1

How about production vertex P ?

P(V’V)

T. Mannel, R. Urech, Z. Phys.C73, 541 (1997); Ulf-G. Meißner, J.Oller, Nucl.Phys. A679 (2001) 671; L. Roca, J. Palomar, E. Oset, H.C.Chiang, Nucl. Phys. A744 (2004) 127F.K.Guo,P.N.Shen, H.C.Chiang, R.G.Ping, Nucl.Phys.A761 (2005) 269

For ’J/ , E small, 1st term dominates higher peak

For , E large, 2nd term dominates lower peak

peak position is process dependent !

P ~ c1 + c2 s

/J

’J/ BES, Phys.Rev. D62 (2000) 032002

BES, Phys.Lett. B598 (2004) 149

Why f0(980)’s peak width is so narrow ?

BES, hep-ex/0411001M = 965 MeVg1 = 165 MeV2

r = g2/g1 = 4.21

r = 0

r = 4.21

Strong coupling toKKstrongly reduce the peak width of f0(980)

B.S.Zou, hep-ph/9611235, “ S-wave interaction and 0++ particles”

0++ particles with substantial couplings to : /f0(600), f0(980), f0(1500), f0(1780-1800)

BES IIPreliminary

/Jf0(1790)

KKJ /?

BES collaboration, hep-ex/0411001

S0pp & I=1 S0pp near threshold enhancement

pmppM 2)(

|M|2BES

elasticelasticM ~|| 2

Both arbitrary normalization

BES, Phys. Rev. Lett. 91, 022001 (2003)

J/ → pp p p p p

COSY-TOF, Eur.Phys.J.A16, 127 (2003)

One-Pion-Exchange and BES pp (1S0) near threshold enhancement Zou B.S., Chiang H.C. Phys.Rev.D69 (2004) 034004

NN interaction :

9 (S , I ) = (0,0) 1 (S , I ) = (1,1)-3 (S , I ) = (1,0) or (0,1) {

NN interaction :

I=0, pp (1S0) gets the biggest attractive force !

deuteron

One exchange FSI & exchange FSI

exchange FSI & full FSI by A.Sibirtsev et al. hep-ph/0411386

A.Sibirtsev, J. Haidenbauer, S. Krewald, Ulf-G. Meißner, A.W. Thomas, hep-ph/0411386

P-waveI=0 s-wave

I=1 s-wave

Pure I = 1

(I=0) + (I=1)

Near threshold enhancement for I=0NN annihilation

E. Klempt, F. Bradamante, A. Martin, J. Richard, Phys. Rept. 368 (2002) 119

BES, Phys. Lett. B472 (2000) 207

PWA Results on J/ to 4

0- +

BES, Phys. Lett. B446 (1999) 356

J/

0-+ resonances decaying to meson channels

0- +

In summary,pp near threshold enhancement is very likely due to some broad sub-threshold 0-+ resonance(s) plus FSI.

3. Ks-wave near threshold enhancement

complimentary BES and COSY experiments

J/P K-vs P P P

P&P the samet-channel interaction

K-& the same interaction

P K- for * P K+ for pentaquarks

)(GeV/c2KΛM

Eve

nts

/10

MeV

Nx

Nx

Nx

)(GeV/c2 MMM KKΛ

PS, eff. corrected

(Arbitrary normalization)

Near-threshold enhancement in MK

BES Collaboration, Phys. Lett. B510 (2001) 75

B.C.Liu and B.S.Zou, Phys. Rev. Lett. 96 (2006) 042002

From relative branching ratios of

J/pN* p (K-p (p

gN*K/gN*p/gN*p~ 1.3 : 1 : 0.6

Smaller N*(1535) BW mass

previous results 0 ~ 2.6 from N and N data

P P P withgN*K/gN*p= 1.3

without N*(1535)K.Tsushima, A.Sibirtsev, A.Thomas, Phys.Rev.C59 (1999) 369

with N*(1535)

(1)

(2)

(3)

Mass of N*(1535)

A.Zhang, Y. Liu, P. Huang, W. Deng, X.Chen, S.L. Zhu, hep-ph/0403210 :

1/2- and 1/2+ octet N* pentaquarks have similar masses in Jaffe-Wilczek diquark model

N*(1535) ~ uud (L=1) + [ud][us]s + …

N*(1440) ~ uud (n=1) + [ud][ud]d + …

*(1405) ~ uds (L=1) + [ud][su]u + …

Larger [ud][us]s component in N*(1535) makes it coupling stronger to N & K, weaker to N & K and heavier ! B.C.Liu, B.S.Zou, PRL 96(2006)042002

ud

du

q

u

du

qSq ½+

[ud][ud]

}L=1

q ½ -[ud][us]

}L=0

Summary for our study on J/P K-and P P P

1) near-threshold enhancement due to N*(1535) with gN*K/gN*p= 1.0 ~ 1.6 compatible with all data

2) Larger [ud][us]s component in N*(1535) makes it coupling stronger to strangeness and heavier !